Device fob computing and indicating



Dec. 24, 1935. TUCKER 2,025,625

DEVICE FOR COMPUTING AND INDICATING TIME INTERVALS Filed Feb. 2, 1934 Patented Dec. 24, 1935 UNITED STATES PATENT OFFICE Gordon Tucker, Minneapolis, Minn, minor to E. Robe Application February 2, 1934, Serial No. 709,512

.22 Claims.

This invention relates to devices for computing and indicating time intervals. Such devices, while not limited thereto, have utility in determining visibly the periods of sterility and fertility of women whose menstrual cycles are known by observation.

For a more complete understanding of the nature of the time intervals capable of computation and indication by devices in accordance with the present invention, as well as of the reasons therefor, reference is made to the work entitled The Rhythm of Sterility and Fertility in Women", Third Edition, 1933, by Leo J. Latz, M. D., published by Latz Foundation, Chicago, Illinois. Briefly, the conclusions reached by Latz and his colleagues in this field of research are to the effect that the menstrual cycle has two periods of sterility and an intermediate period of fertility. The first period of sterility may be regarded as running from the first through the eleventh day, inclusive, preceding the day that menstruation is expected to occur. The fertile period runs from the twelfth day, inclusive, back to the nineteenth day preceding expected menstruation, with the second sterile period running from the twentieth to the beginning of the menses of this cycle and thus completing the cycle.

Thus with a 28-day menstrual cycle and the menses commencing on the first day of the month, the second and first sterile periods are comprised respectively by the days numbered 1 through 9, inclusive, and 18 through 28, inclusive. The fertile period is comprised of the days running from the th to the 17th, inclusive.

The computation of these periods is complicated by the fact that the menstrual cycle of a woman may vary, that is to say, the cycle may occur regularly but at intervals less than or greater than 28 days. Also, the cycle may vary from month to month; that is to say, a 28-day cycle may be followed by a 81-day cycle. In the first condition of variance, the first sterile period (the period in advance of the expected menstruation) and the fertile period are computed in the same manner as in the 28-day cycle above set forth, with the second period of sterility (following the last menstruation) being less or greater as the cycle is less or greater. Under the second condition of variance and under the assumption that the cycle varies between 28 and 31 days, three days must be added to the fertile period to run in addition to the fertile period as computed with a 31-day cycle, so that instead of an 8-day period of fertility this period would be extended to 11 days.

of a device of the above character which indicates 10 visibly the aforementioned periods within a given menstrual cycle. A further object is the provision of a device of the above character which is sufficiently flexible as to compute the periods under consideration within the cycle where the cycle varies of itself or in relation to a following cycle.

Other objects will be in part obvious and in part hereinafter pointed out in connection with the following analysis of this invention, wherein is illustrated one of various possible embodiments of the present invention, together with certain modifications in detail.

In the drawing Fig. 1 is a plan view of the device in accordance with the present invention and set for a regular 28-day menstrual cycle.

Fig. 2 is a section along lines 22 of Fig. 1.

Figs. 3, 4 and 5 are, respectively, detail views of three indicator units shown in assembled relation on the calendar disc in Fig. 1.

Referring to the drawing, reference character l0 indicates a circular calendar disc of suitable material such as cardboard, composition material as bakelite, metal, or the like, having a peripheral band portion II, a calendar portion l2 separated from the band portion by an annular strip l3 of hill and dale" configuration as will be further referred to, and a center portion I 4. By reference to Fig. 2, the disc is centrally apertured as at IS, the aperture receiving the tubular stem l6 of a cup H, with the cup being rigidly fixed to the disc l0.

Referring to the calendar portion I! of the disc, such portion is defined by five concentric circles 20, the circles being equi-distantly spaced and inscribed from the center of disc Ill. The

circles are sub-divided into arcs by the radial lines 2| from the center of the disc, the radii 2| being equi-distantly spaced. The radii divide each of the four angular bands defined by circles 20 into 62 equal segments, with the arc of each segment being 1/62nd of the circumference of the circles.

Numbering the four annular bands from the outer to the inner portion as I, II, III and IV and starting at the line .2, circle I is used for those months of the year that have 31 days (Jannary. March. May, July, August, October and December). Circle 11 isused for those monthsof the year that have'30 days (April, June, Septemher and November).

dicator unit consisting of a hub26 (Figs.i2 and. 3)l

and two angularly dispose'di arrowiarms 21', 2 8, the center lines of whichfsubtend an arcof l8/62nds of the circumference 'of circles 20."' 1In.- termediate their ends. the arrow arms 21, 28 are connected by an arcuate bgi'ndJSiLthe, band ex-' tending substantially beyond arrow 21 in an anticlockwise direction, as at 3|." "The indicator unitthrough the center of disc iili P 25 is mounted to turn mamas which extends seven in number in the'constr'ucti'on illustrated, thus forming six segmental sub-divisions designated as A, B, C, D, E, F. Said radial lines 32 are equi-angularly spaced from each other and their angular spacing corresponds to the spacing of the radial lines 2i aforesaid. The medial line of space F is so related to the center line of arrow arm 21 that as the latter coincides with the medial line of a row of segments of calendar portion iii, the medial line. of spaceor segment F will coincide with that of the next row, in an anti-clockwise direction, oftsegments of the calendar portion.

Intermediate the arrowarms21, 28' the arcuate band is provided with sub-divisions or segments defined by radial lines 33, of which segment 34 is 3/62nds of the circumference, segment 35 is 4/62nds of the circumference, and segment 35, is 2/62nds of the circumference. Segmental division 36 may be designated by the marking G, fol-' lowing which, in a clockwise direction, are the segments 31, marked H, I, J,K, L, each following an arc of 1/62nd of thecircumference. The aforesaid segmental portions are so related to the center line of arrow arm 21 that when this center line coincides witha medial line of a row of segments in the calendar portion, the radial lines 33, if extended, would coincide with radial lines 2| which define said segments. The arcuate band 30 and the extension 3i may be provided with edge flanges 29 and 39, respectively, which extend relatively upwardly, and inwardly to form a guide and retaining trackway for the purpose to-be described.

1A second indicator unit, also movable on an axis extending through the center of the disc, is generally indicated at 40 and comprises a hub 4i (Figs. 2 and 4) an arrow arm 42 extending therefrom, and an arcuate or segmental band 43 offset from and extending intermediate the ends of the arrow arm in a clockwise direction. Said extension 43 is adapted to overlap the extension 3i of indicator unit 25 with' the unit 40 being adjustable thereover and guided by the trackway formed by flanges 39. On the under face of the extension 43 is a lug or detent 44 adapted to fit into depressions or apertures 45 formed the segmental Circle III is used for the month of Februaryduring leapyear, a 29-day calehdarlabove, described, reference character 25 indicates an in-,

acaaeas divisions A to F inclusive, and it will be understood that, as indicator unit 40 is pressed towards the and 40 are heldin desired adjusted position with 5 respect to eachiother. .The, arrow arm 42 may contain markings such as 3|, 30,29, 28 which relate to circles I, II, III and IV, to indicate clearly the number of .days inthe month comprehended with the respective circles. 1 A third indicatorunit, also movable on an axis extending through the center of the disc, may comprise a hub 41 (Figs..2 and with an arrow arm extending therefrom and an arcuate or segmental band 50 offset from and extending from said armintermedlate its ends and in a clockwise direction. Said segmental portion 50 is arranged to overlap the arcuate band 30 of indicator unit 25,-with'the unit 46 being adjustable thereover and guided by the trackway formed by flanges 29. The said portion 50 isprovided on its under face with a detent 5i adapted to engage in one of a series of depressions or apertures 52 formed in cer tain of the segments 31 of arcuate band Hand in a portionof the band adjacent thereto. As unit p V 43 is pressed towards the face of disc l0, it'will, by The extension 3i of the arcuateLband has inscribed thereon a.pluralityj of"radial'lines 32,,

engagement of detent Si in a depression 52, be held in desired adjusted position on unit 25.

Considering now the mounting of the various indicator units of the calendar disc 10, one such 30 form of mounting is illustrated in Fig. 2 and may be described as follows: The hubs 26, 4i and 41 of units 25, 40 and 46, respectively, are mounted on a sleeve 55 having an endflange 53 against which hub 41 may bear. Hubs 4i and 41 are rotatable on said sleeve while hub 26 may be fixed thereto. A spring cap 51 is fixed to sleeve 55 by. bending over the end of the sleeve, as indicated at 58, or by other suitable means. The spring cap 51 is provided on its outer circular wall with a plurality of teeth or serrations 60 which are adapted to interfit with like teeth or serrations formed in a vertical wall of the cup l1 secured to the disc iii. The spring construction of cap 51 cup with the teeth or serrations preventing free turning of the cap relative to the cup i1.

Sleeve and cap 51 are removably secured to the cup'by means of a stud 6i extending there- 50 through and having its end threaded as at 62 to engage with threads formed in the bore of stem IS. The other end of stud 6i has secured thereto a knurled or equivalent nut 64 through the medium of a screw 65. 55

By the aforesaid assembly, the sleeve 55 with the indicator units carried thereby and the spring cap 51 are rotatably carried by stud 6 I. To mount the indicator units on the disc iii, the spring cap 51 is pressed into the cup i 1 and the stud 6i forced through sleeve 55 until its end threads engage the threads on the hollow stem l5, whereupon stud 6| is turned. Consequently, the entire mounting assembly will be secured fast to the cup i1 and disc Ill. 65

When it is desired to reset the indicator and particularly .indicator unit 25, nut 64 is turned to unthread stud 6i whereupon the sleeve 55 and aosaeas metal and their outer ends bowed. Thus, as nut 44 is tightened. and with the various arrows set in their proper position, the hubs of the indicator units are moved axially. with the face of the disc preventing such movement of the ends of the arrow. Accordingly, the free ends of the arrow arms are put under strain and by this means are frictionally held in said position against the face of the disc. Further, the length of the arrow arms is such that their spring ends engage, when properly set, in the depressions of the "hill and dale" strip ll formed in disc i0. Consequently. inadvertent or unintentional movement of the arrow arms. after proper setting, is impossible.

Locking of the indicator unit may be further accomplished through the medium of a pin 88 carried at the free end of a leaf spring 88 riveted or otherwise secured to said unit and preferably to the arrow arm 21 thereof. the locking pin 88 extending through a suitable aperture in the unit and being of sufficient length as to engage in one of a series of holes Ill punched in the central portion l4 of disc Ill. The pin 88 may drop into one of the holes 10 as the unit 25 is brought to desired position of adjustment and thus holds the parts against relative rotation.

In use of the device aforesaid, the setting of the device to arrive at the computations and indications contemplated will now be explained,

.with the setting illustrated in Fig. 1 being that for a regular 28-day cycle. In this setting I have departed somewhat from the findings of Latz above referred to in that while Latz maintains that a period of sterility of 11 days exists prior to the day when menstruation is expected, I have, to provide an added factor of safety, cut down this period to ten days. In further explanation, my device is capable of computing the periods of sterility and fertility for menstrual cycles of 26 to 31 days, inclusive, with the segments A, B, C. D. E, F representing the 31, 80, 29. 28, 2'7 and 26 day cycles, respectively. Assuming that a128-day cycle has been determined by observation, unit 40 is moved over extension segment ii and guided by the flanges 39 thereof to cover the segmental portion C (29-day cycle) and uncover the portion D (28-day cycle) and with unit 48 held to unit 28 in this adjusted relation, as permitted by the mounting of the parts as aforesaid, the device is now ready to indicate the computations arrived at. For this condition of a regular menstrual cycle, unit 48, which is carried on unit 25, has been set to cover segments H-L inclusive, and to uncover segment G, which setting is the same for regular cycles, regardless of their length.

Assuming that menstruation commences on the second day of a 31-day month, the indicating units 25 and 40 are moved about the axis of disc ill until arm 42 indicates the second day of circle I (31-day month). Under this condition arrow arms 42 and 21 define an arc of 10 days, that is. the second day through the tenth day, representing the second sterile period, previously mentioned. Segments 34, 35, 38 define an arc of nine days, that is, from the eleventh through the nineteenth day. This are indicates the days included in the period of fertility, and segments 34, 35 and 38 may be suitably colored and marked to make this period and the days included therein readily distinguishable. If desired, the segment 35 may carry suitable indicia such as "Most Fertile. which will indicate fourv days (the fourteenth through the seventeenth), indicating the most fertile sub-division of the fertile period.

Arrow arms 48 and 28 define an arc of ten days, that is. from the twentieth inclusive through the twenty-ninth day and represents the days included in the first sterile period as referred to in the foregoing. The aforesaid completes the menstrual cycle with the expected menstruation to commence on the thirtieth day of the month.

Where the menstrual cycle is less or greater than the 28-day cycle above treated but with the cycle regular, indicator unit is moved relatively of unit 25, with the result that the second sterile period is increased or decreased while indicator unit is undisturbed due to the observed regularity of the cycle. Thus, if a regular cycle of 30 days has been observed, unit 48 is shifted to cover segment A, but to uncover segment B, and such a setting will lengthen the second sterile period by two days. Conversely, if a 26-day cycle has been observed, unit 48 is shifted to cover segment E, so leaving uncovered the segment F which indicates the 26-day cycle, with the result that the second sterile period is correspondingly shortened.

It will be understood that the setting of the device for a regular cycle with menstruation 'to commence in a 30-day month, or in February of leap year, or in February of intermediate years, the same operations of setting the unit 48 relative to unit 25 and of adjusting said units to the day on which menstruation is to commence is the same as that considered above, although readings in those cases will be made on circles II, III and IV, respectively, rather than on circle I.

Considering now the use of the device of the present invention where the cycle may vary from month to month. unit 48 is adjusted with respect to unit 25 to give an indication of the fertile period. If. for example. the cycle has been found to vary from a 28-day cycle to a 31-day cycle, a difference of three days, unit 40 is adjusted to the 28-day cycle as if the cycle were regular as aforesaid, by covering segment C and uncovering segment D. Thereupon, unit 48 is adjusted in a clockwise direction to uncover three segments, H. I, J, with the result that the fertile period is extended for three days, and under the assumption of the menses commencing on the 2nd day of the month, the fertile period under the condition of irregularity above set forth, will run from the eleventh through the twenty-second day. It will be observed that arrow arm 28 does not move to complete the possibly long cycle of 31 days which might occur, but inasmuch as the fertile period is well established, and as the first sterile period runs to the expected menstruation.

whether it occurs on the 28th or the 31st day,

such is not particularly material. However. where such an added indication is desired, unit 48 could be extended and provided with an additional arrow arm so reiatedas to overlie arrow arm 28 when unit 48 is adjusted for a condition of regularity, that is, as shown in Fig. 1 and as previously described. Thus, as unit 46 is moved clockwise for a one-day, two-day, or greater observed irregularity, the additional arm would move past arrow arm 28 to indicate the day when the cycle is to be complete. with the menses commencing on the day following.

Without further analysis the foregoing will so fully reveal the gist of this invention that others can by applying current knowledge readily adapt it for various applications without omitting certain features that, from the standpoint of the prior art, fairly constitute essential characteristics of the generic or specific aspects of this invention, and therefore such adaptations should and are intended to be comprehended within the meaning and range of equivalency-of the following claims.

I claim: 1

1. In a device of the character described, a disc having a circular band thereon subdivided into a plurality of segments, the segments being numbered serially, and a plurality of indicator units mounted to turn on an axis extending through the center of the disc, one of said units including an arcuate band, a second unit including an arcuate band adapted to be adjustably related to an end portion of said first-named band and an indicator arm extending to said circular band, the firstnamed arcuate band having provisions for establishing a plurality of said numbered segments in relation to a determined segment established by said indicator arm.

2. In a device of the character described, a disc having a circular band thereon subdivided into a plurality of segments, the segments being numbered serially, an indicator unit mounted to turn on an axis extending through the center of the disc, said unit including an arcuate band and an indicator arm extending to said circular band, and a second indicator unit including an arcuate band adapted to be adjustably related to an end portion of said first-named arcuate band and an indicator unit extending in the direction of said numbered segments, said first-named arcuate band having provisions for establishing a plurality of said numbered segments in relation to -a determined segment established by the position of the indicator arm of said second unit.

3. In a device of the character described, a disc having a circular band thereon subdivided into a plurality of segments, the segments being numbered serially, an indicator unit mounted to turn on an axis extending through the center of the disc, said unit including an arcuate band and an indicator arm extending intermediate the ends of said band to said numbered segments, and a second indicator unit including an arcuate band adapted to be adjustably related to one end portion of the first-named arcuate band and an indicator arm extending to said numbered segments, the other end portion of said first-named arcuate band having provisions for establishing a plurality of said numbered segments in relation to a determined segment established by the position of the indicator arm of the second unit.

4. In a device of the character described, a disc having a circular band thereon subdivided into a plurality of segments, the segments being numbered serially, and a plurality of indicator units mounted to turn on an axis extending through the center of the disc, one of said units including an arcuate band, a second unit including an arcuate band adapted to be adjustably related to an end portion of said first-named band and an indicator arm extending to said circular band, the first-named arcuate band having provisions for establishing a plurality of said numbered segments in relation to a determined segment established by said indicator arm, and a third indicator unit including an arcuate band adapted to be adjustably related to the other end portion of said first-named arcuate band and cooperating with said provisions to increase the number of said segments established thereby.

' 5. In a device of the character described, a disc having a circular band thereon subdivided into a plurality of segments, the segments being numbered serially, an indicator unit mounted to turn on an axis extending through the center of the disc, said unit including an arcuate band and an indicator arm extending to said circular band. and a second indicator unit including an arcuate band adapted to be adjustably related to an end portion of said first-named arcuate band and an 5 indicator arm extending in the direction of said numbered segments, said first-named arcuate band having provisions for establishing a plurality of said numbered segments in relation to a determined segment established by the position of the indicator arm of said second unit, and a third indicator unit including an arcuate band adapted to be adjustably related to the other end portion of said first-named arcuate band and cooperating with said provisions to increase the number of said segments established thereby.

6. In a device of the character described, a disc having a circular band thereon subdivided into a plurality of segments, the segments being numbered serially, an indicator unit mounted to turn on an axis extending through the center of the disc, said unit including an arcuate band and an indicator arm extending intermediate the ends of said band to said numbered segments, and a second indicator unit including an arcuate band adapted to be adjustably related to one end portion of the first-named arcuate band and an indicator arm extending to said numbered segments, the other end portion of said first-named arcuate band having provisions for establishing a plurality of saidnumbered segments in relation to a determined segment established by the position of the indicator arm of the second unit, and a third indicator unit including an arcuate band adapted to be adjustably related to the other end portion of said first-named arcuate band and cooperating with said provisions to increase the number of said segments established thereby.

'7. In a device of the character described, a disc having a circular band thereon subdivided into a 40 plurality of segments, the segments being numbered serially, an indicator unit mounted to turn on an axis extending through the center of the disc, said unit including an arcuate band and an indicator arm extending to said circular band, a second indicator unit comprising an indicator arm extending to said circular band and an arcuate band adapted to be adjustably related to one end portion of the first-named arcuate band whereby said indicator arms may define an are of said circular band as permitted by said adjustment, and a third indicator unit including an indicator arm extending to said circular band and adjustably related to the other end portion of the first-named arcuate band, said indicator arms of the first and third-named units establishing a plurality of said numbered segments in relation to a segment-established by the indicator arm of the second-named unit.

8. In a device of the character described, an element having a circular calendar portion comprising four concentric bands and the bands being each subdivided into sixty-two equal segments, with the segments of the bands being disposed radially, the segments of the bands being further numbered serially from a common radius in accordance with the four length conditions of adjacent months of the year, and a plurality of indicator units mounted to turn on an axis extending through the center of the calendar por- 'tion, one of said units being settable with relation to another unit, and along a radial row of segments, and said other unit defining an arc along said calendar portion, whereby to establish a,oss,eas

a period of a plurality oi. numbered days within said are.

'9. In a device of the character described, an element having a circular calendar portion comprising tour concentric bands and the bands being each subdivided into sixty-two equal segments, with the segments of the bands being disposed radially, the segments of the bands being further numbered serially from a common radius in accordance with the tour length conditions of adjacent months of the year, and a plurality of indicator units mounted to turn on an axis extending through the center 01' the calendar portion, two or said units being settable with relation to a third unit, whereby to establish a period of a plurality oi numbered days within an are along said calendar portion as indicated by two of said units.

10. In a device the character described, an element having a circular calendar portion comprising tour concentric bands and the bands being each subdivided into sixty-two equal segments, with the segments of the bands being disposed radially, the segments 01' the bands being further numbered serially from a common radius in accordance with the four length conditions of adjacent months of the year, and a plurality of indicator units mounted to turn on an axis extending through the center oi. the calendar portion, two of said units being carried by and settable with relation to a third unit, whereby to establish a plurality of numbered days within an are along said calendar portion as indicated by two of said units.

11. In an indicator, a data carrying element having *a mounting member, a sleeve, a plurality of indicator units, one of said units being fixed to the sleeve and another unit being carried by said first unit and rotatable on the axis of the member, and means for securing detachably the sleeve to the member.

12. In an indicator, a data carrying element having a mounting member, a sleeve, a plurality of indicator units, one of said units being fixed to the sleeve and another unit being carried by said first unit and rotatable on the axis of the member, a cap fixed on the sleeve and seating in the mounting member, and means for securing detachably the cap to the mounting member.

18. In an indicator, a data carrying element having a mounting member, a sleeve, a plurality of indicator units, one of said units being fixed to the sleeve and another unit being carried by.

said first unit and rotatable on the axis of the member, a cap fixed on the sleeve and adapted to seat in the mounting member, means cooperating between the cap and the member whereby to hold said first unit in desired angular position, and means for actuating said cap axially of said member whereby to seat the cap in the member.

14. In an indicator, a data carrying element having a mounting member, a sleeve, a plurality of indicator units, said units having portions of springy material adapted to engage said element, one of said units being fixed on said sleeve, another unit being carried by said first unit and rotatable on the axis or the sleeve, and means for actuating the sleeve and units axially against the resistance of the springy material of said units to said actuation, said means being operative to secure the sleeve to the mounting member and to resiliently hold the units in desired position relative to the data carrying element.

15. In an indicator, a data carrying element,

numbered serially ifrom an an indicator unit rotatable on an axis extending through said element, means for securing detachably the unit to the element including provisions for actuating the unit in the direction or the axis on which it is rotatable. and means responsive to such actuation to hold the unit against rotation on said axis.

16. In an indicator, a data carrying element, an indicator unit rotatable on an axis extending through said element, means for securing dotachably the unit to the element including pro-. visions for actuating the unit in the direction or the axis on which it is rotatable, and cooperating means on said element and said unit and responsive to such actuation to hold the unit is against rotation on said axis.

17. In an indicator, a data carrying element,

a mounting cup secured thereto and having serrations on its inner wall, an indicator unit, and means carrying said unit and having provisions go cooperating with the serrations oi the cup for holding the unit against rotation.

18. In a device of the character described, an element providing a circular band subdivided into a plurality of segments, the segments being numbered serially, an indicator unit movable on said element, said unit providing a band portion cooperatively related to said circular band, a second indicator unit adjustably related on said first unit and having an indicator for indicating a segment of said circular band and the firstnamed unit having provisions for establishing a plurality of numbered segments on said circular band in relation to a determined segment established by the indicator of said second unit.

19. In a device of the character described, an element providing a circular band subdivided into a plurality of segments, the segments being numbered serially, an indicator unit movable on said element, said unit providing a band portion cooperatively related to said circular band, a second indicator unit adjustably related on said first unit and having an indicator for indicating a segment 01' said circular band, and a third indicator unit adiustably related on said first unit, said first and third units each provided with an indicator operative to establish therebetween a plurality of numbered segments on said circular band in relation to a determined segment established by the indicator of said second unit.

20. In a device of the character described, an element providing four concentric bands and the bands being each subdivided into sixty-two equal segments, with the segments 01' the bands being aligned, the segments of the bands being further numbered serially from an aligned row of segments in accordance with the tour length conditions of adjacent months of the year, and a plurality oi indicator units mounted for movement on said element, one 01' said units being 00 settable with relation to another unit to designate the aligned segments 01' a row and said other unit establishing a plurality of segments along the arc of the bands and in relation to a segment of the row of segments designated by said first unit.

21. In a device of the character described, an element providing tour concentric bands and the bands being each subdivided into sixty-two equal segments, with the segments oi the bands being 7 aligned, the segments or the bands being further aligned row of segments in accordance with the four length conditions of adjacent months oi the year, and a pinrality oi indicator units mounted ior movement 7 on said element, two of said units being 'settable with relation to a third unit whereby to establish a period of a plurality of numbered days along the arc of the bands as indicatedby two of said units-in relation to another unit.

22. In a device of the character described, an element providing four concentric bands and the bands being each subdivided into sixty-two equal segments, with the segments of the bands being aligned, the segments of the bands being further numberedserlally from an aligned row of seg- 

